Journal
DISCRETE APPLIED MATHEMATICS
Volume 157, Issue 6, Pages 1309-1318Publisher
ELSEVIER
DOI: 10.1016/j.dam.2007.08.044
Keywords
Hartree-Fock; Global optimization; Branch-and-Bound
Categories
Funding
- FAPERJ
- FAPESP
- CNPq
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This paper concerns the application of reformulation techniques in mathematical programming to a specific problem arising in quantum chemistry, namely the solution of Hartree-Fock systems of equations, which describe atomic and molecular electronic wave functions based on the minimization of a functional of the energy. Their traditional solution method does not provide a guarantee of global optimality and its output depends on a provided initial starting point. We formulate this problem as a multi-extremal nonconvex polynomial programming problem, and solve it with a spatial Branch-and-Bound algorithm for global optimization. The lower bounds at each node are provided by reformulating the problem in such a way that its convex relaxation is tight. The validity of the proposed approach was established by successfully computing the ground-state of the helium and beryllium atoms. (C) 2007 Elsevier B.V. All rights reserved.
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